Logaritmer - forenkle uttrykk 3 - Numbas at mathcentre.ac.uk

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Question statement

Forenkle uttrykket.

Give any introductory information the student needs.

			Name	Type	Generated Value

c	list	[ 3, 7, 4, 5, 3, 5 ]
ex	list	[ 1, 5 ]
b1	number	2
b2	number	32
ka	integer	7
kb	integer	10
k2	integer	-4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(2..7),6)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 3, 7, 4, 5, 3, 5 ]

→ Used by:

Parts

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Advice

Her bruker vi logaritmesetningene:

$\ln(ab)=\ln(a)+\ln(b)$
$\ln\left(\dfrac{a}{b}\right)=\ln(a)-\ln(b)$
$\ln\left(a^{b}\right)=b\ln(a)$

I tillegg bruker vi sammenhengen $\ln(e)=1$ .

Vi skal forenkle uttrykket

$\ln\left(\var{b1}a^{\var{c[0]}}\right)-\ln\left(\dfrac{b^{\var{c[1]}}}{a^{\var{c[2]}}}\right)+\ln\left(\dfrac{e^{\var{c[3]}}}{\var{b2}b^{\var{c[4]}}}\right)$

Her kan det være en fordel å forenkle hvert ledd for seg først:

$\ln\left(\var{b1}a^{\var{c[0]}}\right)=\ln(\var{b1})+\ln(a^{\var{c[0]}})=\ln(2^{\var{ex[0]}})+\var{c[0]}\ln(a)=\var{ex[0]}\ln(2)+\var{c[0]}\ln(a)$
$\ln\left(\dfrac{b^{\var{c[1]}}}{a^{\var{c[2]}}}\right)=\ln(b^{\var{c[1]}})-\ln(a^{\var{c[2]}})=\var{c[1]}\ln(b)-\var{c[2]}\ln(a)$
$\ln\left(\dfrac{e^{\var{c[3]}}}{\var{b2}b^{\var{c[4]}}}\right)=\ln(e^{\var{c[3]}})-\ln(\var{b2}b^{\var{c[4]}})=\var{c[3]}\ln(e)-\left(\ln(\var{b2})+\ln(b^{\var{c[4]}})\right)=\var{c[3]}-\ln(2^{\var{ex[1]}})-\ln(b^{\var{c[4]}})=\var{c[3]}-\var{ex[1]}\ln(2)-\var{c[4]}\ln(b)$

Så setter vi sammen:

$\ln\left(\var{b1}a^{\var{c[0]}}\right)-\ln\left(\dfrac{b^{\var{c[1]}}}{a^{\var{c[2]}}}\right)+\ln\left(\dfrac{e^{\var{c[3]}}}{\var{b2}b^{\var{c[4]}}}\right)\\ =\var{ex[0]}\ln(2)+\var{c[0]}\ln(a)-\left(\var{c[1]}\ln(b)-\var{c[2]}\ln(a)\right)+\var{c[3]}-\var{ex[1]}\ln(2)-\var{c[4]}\ln(b)\\ =\var{c[0]}\ln(a)+\var{c[2]}\ln(a)-\var{c[1]}\ln(b)-\var{c[4]}\ln(b)+\var{ex[0]}\ln(2)-\var{ex[1]}\ln(2)+\var{c[3]}\\ =\underline{\underline{\var{ka}\ln(a)-\var{kb}\ln(b)+\var{k2}\ln(2)+\var{c[3]}}}$

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This question is used in the following exam:

Logaritmer by Torris Bakke in UiT forkurs.

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Logaritmer - forenkle uttrykk 3

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Taxonomy: mathcentre

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Taxonomy: Context

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Torris Bakke 1 month, 3 weeks ago

Torris Bakke 2 months ago

Torris Bakke 2 months ago

Error in variable testing condition

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Generated value: `list`

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Logaritmer - forenkle uttrykk 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Torris Bakke 1 month, 3 weeks ago

Torris Bakke 2 months ago

Torris Bakke 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`